Formulas for interest Interest

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The discussion centers on the confusion surrounding the correct application of the compound interest formula. The formula presented, P=A(1+(r/n)^(rt)), is debated, with a clarification that the correct expression should be P=A(1+(r/n))^(nt) for annual compounding. A user suggests simplifying calculations by expressing the interest rate as 1.09 for easier memory retention. The importance of knowing whether the interest is simple or compounded, and the frequency of compounding, is emphasized as crucial for accurate calculations. Overall, understanding the correct formulas and their applications is vital for solving interest-related problems effectively.
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Today I was watching my sister do her Financial homework and I tryed to do one of them problems it said something about haveing 5000 bucks at 9% interest for 6 years and you had to find how much you would have.

And so I tryed to use the compound interest formula P=A(1+(r/n)^rt but we both got totaly different anwers. She did it on a standar issued financial caculator.

So is that the formula for compound interest? P=A(1+(r/n)^rt. And is this how you plug it in? P=5,000(1+(.09/6)^(.09*6)

Also what are other interest raletaed equations and state what goes in the variables.

All the other ones that I know are:

Compound Interest: P=A(1+(r/n)^rt

Compound Interest Continusly: P=e^rt

Rule of 72

Rule of 82

Simple Interest: You don't really need a formula for this one, all that happens is that your you only earn interest on your original amound earns interst.
 
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The formula for compound interest is: P(1+\frac{r}{n})^{nt} not P(1+\frac{r}{n})^{rt} So:

A = 5000(1+\frac{0.09}{1})^{6} = 8385.5, assuming that it is returned once per year.
 
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I never remember the compound interest formula. I just express a 9% increase as 1.09. Then the answer just becomes 5000(1.09^6)

I just find this method easier to remember tbh..although it's basically the same thing.
 
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That's assuming it is compounded annually. Surely the problem said something more than just "5000 bucks at 9% interest for 6 years". Didn't it say something like "simple interest" or "compounded monthly", "compounded annually", etc.?
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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